An optimal response adaptive design for multi-treatment clinical trials with ordinal categorical outcomes

ABSTRACT

In clinical trials, fixed randomizations in a prefixed proportion (e.g. 1:1 or 2:1 for two treatment trials) may be adopted to allocate the entering patients among the competing treatments. However, such an allocation procedure ignores the knowledge obtained from the accrued information on the performance of the treatments until that point. However, while allocating, a fixed randomization may favor the most and the least effective treatments in a prefixed manner, and hence becomes instrumental to induce a conflict with the “individual ethics” requirement. Adaptive allocation designs are considered instead, for their ability to dynamically settle the issue of running randomization towards the treatment doing better – all using the available data but with a scope to compromise in statistical precision. Although most of the developments are pertinent to binary, continuous and survival responses, ordinal categorical responses are natural outcomes in many disciplines of clinical trials like Orthopedics and Ophthalmology. Therefore, to balance between ethics and precision in the context of a multi-treatment clinical trial producing ordinal categorical responses, an optimal response adaptive design is derived by minimizing a measure of “precision” subject to constrained number of “failures” ensuring higher number of assignments to the “best” treatment. Related design and inference-based characteristics are extensively studied – both theoretically and empirically. Further, the practical applicability of the developed design is envisaged through re-designing of a real clinical trial, where the responses are immediate and are measured in ordinal categorical scale.

KEYWORDS:

• Optimality
• response adaptive randomization
• categorical response

Acknowledgments

The authors are grateful to the anonymous referees and the Associate Editor for providing helpful comments, which have led to significant improvement over an earlier version of this work.